Let G be a complex reductive algebraic group and let Gamma be a finitely
generated group. We study irreducible and completely reducible representations
rho: Gamma -> G in the context of the geometric invariant theory of the
G-action on Hom(Gamma,G) by conjugation.

Additionally, we study properties of character varieties, Hom(Gamma,G)//G. In
particular we describe the tangent spaces to X_G(Gamma) in terms of first
cohomology groups of Gamma with twisted coefficients, generalizing the well
known formula.

Let M be an orientable 3-manifold with a connected boundary F of genus > 1.
Let X_G^g(F) be the subset of the G-character variety of F composed of
conjugacy classes of good representations. By a theorem of Goldman, X_G^g(F) is
a holomorphic symplectic manifold. We prove that the set of good
G-representations of pi_1(F) which extend to representations of pi_1(M) is an
isotropic submanifold of X_G^g(F). If these representations correspond to
reduced points of the G-character variety of M then this submanifold is
Lagrangian.